In 1976, Richard Skemp published a 16 page article on the teaching of mathematics and, in particular, ‘relational’ and ‘instrumental’ understanding. By ‘relational understanding’ he meant ‘knowing both what to do and why’. Whereas he refers to ‘instrumental understanding’ as ‘rules without reasons’. He notes that for many pupils (and their teachers) just knowing the rules may well be sufficient because the pressure is to get good exam results. Knowing the formula gets right answers – you can use it even if you don’t know why it works. But Skemp believes any good teacher would want the pupils to understand relationally – the why as well as the how – and that with careful lesson planning this can be done.
In 2010, Dan Meyers created a TED talk on … in essence relational understanding and instrumental understanding in Mathematics; in effect the video from Meyers is a modern presentation of Skemp’s previous views. So why, after nearly 40 years between the article and TED talk, are we still having this discussion? Why has little changed? I feel we all know that more problem solving and patterns should be introduced at some level into modern mathsand yes I agree with them both! We should be leaning towards rational learning and exploring mathematical ideas through problem solving.
There is only one major difference between the two pieces – that is how this information was given to us! Skemp’s is in the old format of written words, on a plain white page – whereas Meyer’s is on the internet via a TED talk, reaching a global audience through use of audio, pictures and colours (which I found much more engaging). So isn’t this exactly the transformation that now needs to take place in our Maths curriculum? Move away from books and paper and rely more upon experiments and technology through relational learning.
In 1976, Richard Skemp was speaking in a period when there was limited access to technology and digital platforms. It would have been near impossible to plan an exercise on the ‘time it takes for a water tank’ to fill up! It would have been impractical and time consuming. The challenge of regularly teaching in a relational way would have been HUGE because of the time commitment and limited resources available. Therefore instrumental learning has always been heavily relied upon because it was easiest and led to best exam results.
But now, 40 years on, perhaps we can make this change. In our modern age it is more feasible than ever to start to lean towards a more relational way of teaching because we now have multiple platforms of learning. Currently in some schools every student has access to an Ipad, the technology is right in front of them!
Hopefully in another 40 years this debate would be unimaginable – all teachers will be actively using relational understanding in a problem solving, pattern based mathematics curriculum, using the instrumentals only as guidance in classrooms if needed. Instead of ‘selling a product to a market that doesn’t want it but forced to buy It’ students will want to buy into maths because its new, current and exciting. Our generation of Maths teachers can change the view on Mathematics and that for me is one of the reasons I would like to become a teacher. We have the opportunity to make a real difference.